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Re: How can I make the output value of Interpolation[] preciser?


liwen liwen wrote:
> 
> Dear Friends:
>              How are you!
>              I want to increase the effective digits
> for the output value of Interpolation[] so
> that it will be preciser .For example:
> 
> tab={{0,0},{0.25,0.255342},{0.5,0.546302},{0.75,0.931596},{1,1.55741},{1.25,3.00957},
> {1.5,14.1014},{1.75,-5.52038}};
> Cha=Interpolation[tab];
> In[1]:x=Cha[0.674];
> Out[1]:x=0.795744
> 
> I want to make the output value be preciser,for
> example ,0.795744032781,so I modified the value of
> {0.5,0.546302}
> to be {0.5,0.5463024567854}and {0.75,0.931596} to be
> {0.75,0.93159637289321},but the output value of
>  Cha[0.674] does not turn to be preciser,it still
> keeps 0.795744 ,what can I do?
> 
> Best Regards,
> 
> Liwen E-mail: gzgear at yahoo.com


Er, what exactly do you want from these numbers? More digits to look at?
For that you could use InputForm or other print formatting techniques.

Do you expect to obtain more digits that mean something? You can
rationalize the input, make an interpolation perhaps to higher order,
but lacking very strong assumptions on the regularity of the data, there
is no grounds to expect more than a few digits or so to "correctly"
model whatever might be the implicit underlying function. Hence without
such information it makes little sense to treat many digits of y-values
at intermediate points as significant, regardless of how precise are the
values at the knots.

This limitation is numerical analysis, pure and simple. It is not
realistic to expect the software to magically produce significant digits
from thin air. I admit we do that sort of thing from time to time, but
then we fix the bugs.


Daniel Lichtblau
Wolfram Research


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